In the context of our framework, \(f_i\)  denotes the loss for task \(\mathcal {T}_i\) , \(x\)  denotes the weights of the embedding network, and \(y_i\)  denotes the task-specific weights for task \(i\) . We remark that the framework in [1]} is unable to handle this problem because their framework requires the problem dimension of each of the inner tasks to be identical, i.e., \(d_2^i = d_2^j\forall i,j \in [n]\) . However, in our framework, \(y_i \in \mathbb {R}^{d_2^i}\)  may have different dimensions for each task \(i\).
